volume | PIER Journals

Abstract

The study investigates the mathematical background of the method of auxiliary sources (MAS) employed in electromagnetic diffraction. Here, the mathematical formulation is developed for E-polarized plane wave diffraction by perfectly conducting two-dimensional objects of arbitrary smooth shape, and the comparison with an analytical and a numerical approach is provided in the numerical part. The results reveal a quite high accuracy among all methods. The importance of the study is to develop the complete mathematical background of MAS for two-dimensional TM-polarized electromagnetic scattering problems by conducting objects. Different from the method of moments (MoM) and other integral equation approaches in electromagnetic scattering problems, here the integral equation resulting from the boundary condition on the scatterer is solved by expanding the current density as orthonormalized Hankel's function with the argument of the distance between the scatterer actual and auxiliary surfaces. The approach can be summarized by that first the sources are shifted inside the scatterer and second, the boundary condition is employed as the total tangential electric field is zero on the surface and inside the object. Then, such expansion leads to eliminating the singularity problems by shifting the sources from the actual surface.

1. Karacuha, K., "General approach to the line source electromagnetic scattering by a circular strip: Both E- and H-polarisation cases," IET Microwaves, Antennas Propag., 2021.

2. Sefer, A. and A. Yapar, "Inverse scattering by Perfectly Electric Conducting (PEC) rough surfaces: An equivalent model with line sources," IEEE Trans. Geosci. Remote Sens., Vol. 60, 2022.

3. Sever, E., Y. A. Tuchkin, and F. Dikmen, "On a superalgebraically converging, numerically stable solving strategy for electromagnetic scattering by impedance cylinders," J. Comput. Electron., Vol. 17, No. 1, 427-435, 2018.
doi:10.1007/s10825-017-1073-9

4. Dogan, M., F. Dikmen, and A. Alkumru, "Line source diffraction by perfectly conducting successive steps," Wave Motion, Vol. 68, 253-271, 2017.
doi:10.1016/j.wavemoti.2016.10.004

5. Yildiz, G., et al., "Antenna excitation optimization with deep learning for microwave breast cancer hyperthermia," Sensors, Vol. 22, No. 17, 6343, 2022.
doi:10.3390/s22176343

6. Jeladze, V. B., M. M. Prishvin, V. A. Tabatadze, I. M. Petoev, and R. S. Zaridze, "Application of the method of auxiliary sources to study the in uence of resonance electromagnetic fields on a man in large spatial domains," J. Commun. Technol. Electron., Vol. 62, No. 3, 195-204, 2017.
doi:10.1134/S1064226917030093

7. Tabatadze, V., R. Zaridze, I. Petoev, B. Phoniava, and T. Tchabukiani, "Application of the method of auxiliary sources in the 3D antenna synthesis problems," 2015 XXth IEEE International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED), 85-89, 2015.
doi:10.1109/DIPED.2015.7324261

8. Prishvin, M., L. Bibilashvili, V. Tabatadze, and R. Zaridze, "Supplementary analysis of RF exposure simulations of low-power transmitters," Journal of Electromagnetic Waves and Applications, Vol. 13, No. 1, 58-69, 2011.

9. Tabatadze, V., K. Karacuha, E. Veliyev, E. Karacuha, and R. Zaridze, "The electric field calculation for mobile communication coverage in buildings and indoor areas by using the method of auxiliary sources," Complexity, Vol. 2020, 4563859, 2020.

10. Tabatadze, V., K. Karacuha, E. Karacuha, and R. Zaridze, "Simple approach to determine the buried object under the ground," 2021 IEEE 26th International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED), 177-180, 2021.

11. Kupradze, V. D. and M. A. Aleksidze, "The method of functional equations for the approximate solution of certain boundary value problems," USSR Comput. Math. Math. Phys., Vol. 4, No. 4, 82-126, 1964.
doi:10.1016/0041-5553(64)90006-0

12. Kupradze, V. D., "On the approximate solution of problems in mathematical physics," Russ. Math. Surv., Vol. 22, No. 2, 58, 1967.
doi:10.1070/RM1967v022n02ABEH001210

13. Zaridze, R. S., R. Jobava, G. Bit-Banik, D. Karkasbadze, D. P. Economou, and N. K. Uzunoglu, "The method of auxiliary sources and scattered field singularities (caustics)," Journal of Electromagnetic Waves and Applications, Vol. 12, No. 11, 1491-1507, 1998.
doi:10.1163/156939398X00430

14. Zaridze, R., G. Bit-Babik, K. Tavzarashvili, N. K. Uzunoglu, and D. Economou, "The Method of Auxiliary Sources (MAS) --- Solution of propagation, diffraction and inverse problems using MAS," Applied Computational Electromagnetics, 33-45, Springer, 2000.
doi:10.1007/978-3-642-59629-2_3

15. Zaridze, R. S., V. A. Tabatadze, I. M. Petoev-Darsavelidze, and G. V. Popov, "Determination of the location of field singularities using the method of auxiliary sources," J. Commun. Technol. Electron., Vol. 64, No. 11, 1170-1178, 2019.
doi:10.1134/S1064226919110263

16. Jeladze, V., M. Tsverava, T. Nozadze, V. Tabatadze, M. Prishvin, and R. Zaridze, "EM exposure study on an inhomogeneous human model considering different hand positions," 2016 XXIst International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED), 9-12, 2016.
doi:10.1109/DIPED.2016.7772197

17. Balanis, C. A., Advanced Engineering Electromagnetics, John Wiley & Sons, 1999.

18. Sebak, A. and L. Shafai, "Generalized solutions for electromagnetic scattering by elliptical structures," Comput. Phys. Commun., Vol. 68, No. 1-3, 315-330, 1991.
doi:10.1016/0010-4655(91)90206-Z

19. Gibson, K., "The ovals of Cassini," Lect. Notes, 2007.

Dr. Vasil Tabatadze

Mr. Kamil Karaçuha

Dr. Revaz Zaridze